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Pseudo-spectral methods and linear instabilities in reaction-diffusion fronts.

Wesley B. Jones1, James J. O'Brien

  • 1Advanced Systems Division, Silicon Graphics Inc., Mountain View, California 94043-1389COAPS, Florida State University, Tallahassee, Florida 32306-3041.

Chaos (Woodbury, N.Y.)
|June 1, 1996
PubMed
Summary

The pseudo-spectral Fourier method offers faster convergence and better symmetry preservation for reaction-diffusion equations compared to finite difference methods, aiding pattern formation studies.

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Molecular Constants for the v=0, b(1)Sigma(g)(+) Excited State of O(2): Improved Values Derived from Measurements of the Oxygen A-Band Using Intracavity Laser Spectroscopy.

Journal of molecular spectroscopyยท2001
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Area of Science:

  • Computational physics
  • Chemical kinetics
  • Nonlinear dynamics

Background:

  • Reaction-diffusion equations model complex spatiotemporal phenomena.
  • Cubic autocatalytic models are fundamental in chemical kinetics.
  • Non-equilibrium constraints are crucial for realistic system behavior.

Purpose of the Study:

  • Compare pseudo-spectral Fourier and finite difference methods for reaction-diffusion equations.
  • Analyze numerical method performance in terms of accuracy and symmetry preservation.
  • Investigate pattern formation mechanisms in nonlinear reaction-diffusion systems.

Main Methods:

  • Application of a pseudo-spectral Fourier method.
  • Implementation of a second-order finite difference method.

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  • Utilized the Gray and Scott cubic autocatalytic reaction-diffusion model with a non-equilibrium constraint.

    • Main Results:

    • Spectral method shows more rapid convergence of phase speeds for 1D waves.
    • Spectral method demonstrates superior symmetry preservation in 2D simulations.
    • Identified symmetry breaking linear instability as a route to pattern formation.

    Conclusions:

    • Pseudo-spectral Fourier method is more efficient and accurate for these reaction-diffusion models.
    • Numerical method choice significantly impacts the study of wave propagation and pattern formation.
    • Symmetry breaking instabilities play a key role in generating complex patterns from simple initial conditions.